Velocity distribution of particles in an arbitrary-arrangement of rotating gases

If we have a "quasi-rigid" rotating convective cell where the gas overall rotates at the same angular velocity, we could establish a non-inertial frame of reference co-rotating with this convective cell such that the particles of the gas (seen from that frame of reference) may follow a Maxwell-Boltzmann distribution.

But with what statistical distribution may we characterize the temperature function of a system of gases whose fluid rotations occur around various arbitrary axes and speeds with cells of a varying size, evaluated from an inertial, observing frame? In this case, the particle velocities may or may not follow a Maxwell-Boltzmann distribution.

Will air flowing into a tornado have particle velocity distribution that deviates from the Maxwell-Boltzmann distribution as that tornado increases in speed and rotational rate? Are there any numerical parameters that can be used to usefully characterize the amount of this deviance from Maxwell-Boltzman characteristics for certain kinds of calculations in non-equilibrium thermodynamics?